{
 "cells": [
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   "source": [
    "# Random Signals\n",
    "\n",
    "*This jupyter notebook is part of a [collection of notebooks](../index.ipynb) on various topics of Digital Signal Processing. Please direct questions and suggestions to [Sascha.Spors@uni-rostock.de](mailto:Sascha.Spors@uni-rostock.de).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Auto-Correlation Function\n",
    "\n",
    "[Correlation](https://en.wikipedia.org/wiki/Correlation_and_dependence) is a statistical measure for the dependencies between random processes or between the samples of one random process. The [auto-correlation function](https://en.wikipedia.org/wiki/Autocorrelation) (ACF) characterizes the temporal dependencies within one random signal $x[k]$. It is an important measure for the analysis of signals in communications engineering, source coding and system identification."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Definition\n",
    "\n",
    "For a continuous-amplitude, real-valued random signal $x[k]$ the ACF is defined by the [second-order ensemble average](ensemble_averages.ipynb#Second-Order-Ensemble-Averages) of the signal at two different time-instants $k_1$ and $k_2$\n",
    "\n",
    "\\begin{equation}\n",
    "\\varphi_{xx}[k_1, k_2] = E\\{ x[k_1] \\cdot x[k_2] \\}.\n",
    "\\end{equation}\n",
    "\n",
    "Under the assumption of [wide-sense stationarity](stationary_ergodic.ipynb#Wide-Sense-Stationary-Random-Processes) (WSS) the ACF does only depend on the difference $\\kappa = k_1 - k_2$ between the considered sample indices\n",
    "\n",
    "\\begin{equation}\n",
    "\\varphi_{xx}[\\kappa] = E\\{x[k] \\cdot x[k-\\kappa] \\},\n",
    "\\end{equation}\n",
    "\n",
    "where $\\kappa$ is commonly chosen as sample index instead of $k$ in order to indicate that it denotes a time shift / lag. The ACF quantifies the similarity of a signal with a shifted version of itself. It has high (positive / negative) values for high similarity and low (positive / negative) values for low similarity.\n",
    "\n",
    "If the process is additionally [wide-sense ergodic](stationary_ergodic.ipynb#Wide-Sense-Ergodic-Random-Processes), the ACF can be computed by averaging along one sample function\n",
    "\n",
    "\\begin{equation}\n",
    "\\varphi_{xx}[\\kappa] = \\lim_{K \\to \\infty} \\frac{1}{2K + 1} \\sum_{k=-K}^{K} x[k] \\cdot x[k-\\kappa].\n",
    "\\end{equation}\n",
    "\n",
    "Note that the normalization on the left side of the sum is discarded in some definitions of the ACF. Above summation resembles strongly the definition of the [discrete convolution](https://en.wikipedia.org/wiki/Convolution#Discrete_convolution). For a random signal $x_N[k] = \\text{rect}_N[k] \\cdot x[k]$ of finite length $N$ and by exploiting the properties of a wide-sense ergodic random process one yields\n",
    "\n",
    "\\begin{equation}\n",
    "\\varphi_{xx}[\\kappa] := \\frac{1}{N} \\sum_{k=0}^{N-1} x_N[k] \\cdot x_N[k-\\kappa] = \\frac{1}{N} \\; x_N[\\kappa] * x_N[- \\kappa],\n",
    "\\end{equation}\n",
    "\n",
    "where the ACF $\\varphi_{xx}[\\kappa] = 0$ for $|\\kappa| > N-1$. Hence, the ACF can be computed by (fast) convolution of the random signal with a time reversed version of itself. \n",
    "\n",
    "Note that in numerical implementations (e.g. MATLAB, Python with `mode='full'`), the computed ACF is stored in a vector of length $2 N - 1$. The positive indices $0, 1, \\dots, 2 N - 2$ of this vector cannot be directly interpreted as $\\kappa$. \n",
    "For an interpretation with respect to the actual time lag $\\kappa$, $N-1$ must be subtracted from these indices.\n",
    "\n",
    "Further note that $\\frac{1}{N}$-averaging yields a [biased estimator](https://en.wikipedia.org/wiki/Bias_of_an_estimator) of the ACF, which consistently should be denoted with $\\hat{\\varphi}_{xx,\\mathrm{biased}}[\\kappa]$.\n",
    "The unbiased estimator of the ACF is given as\n",
    "$$\\hat{\\varphi}_{xx,\\mathrm{unbiased}}[\\kappa] = \\frac{1}{N-|\\kappa|}\\sum_{k=0}^{N-1} x_N[k] \\cdot x_N[k-\\kappa].$$"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Properties\n",
    "\n",
    "The following properties of the ACF can be deduced from its definition:\n",
    "\n",
    "1. The ACF $\\varphi_{xx}[\\kappa]$ has a maximum at $\\kappa = 0$. It is given as\n",
    "    \n",
    "    $$ \\varphi_{xx}[0] = E\\{x^2[k]\\} = \\sigma_x^2 + \\mu_x^2 $$\n",
    "    \n",
    "    This is due to the fact that the signal is equal to itself for $\\kappa = 0$. Please note that for periodic random signals more than one maximum will be present.\n",
    "    \n",
    "2. The ACF is a function with even symmetry\n",
    "    \n",
    "    $$ \\varphi_{xx}[\\kappa] = \\varphi_{xx}[-\\kappa] $$\n",
    "    \n",
    "3. For typical random signals, the ACF approaches the limiting value\n",
    "    \n",
    "    $$ \\lim_{|\\kappa| \\to \\infty} \\varphi_{xx}[\\kappa] = \\mu_x^2 $$\n",
    "    \n",
    "    The similarity of a typical random signal is often low for large lags $\\kappa$.\n",
    "\n",
    "4. The ACF of a periodic signal $x[k] = x[k + P]$ is also periodic\n",
    "\n",
    "    $$ \\varphi_{xx}[\\kappa] = \\varphi_{xx}[\\kappa + P] $$\n",
    "    \n",
    "    with the period $P \\in \\mathbb{N} \\setminus 0$\n",
    "\n",
    "A random signal $x[k]$ is said to be **uncorrelated** if\n",
    "\n",
    "\\begin{equation}\n",
    "\\varphi_{xx}[\\kappa] = \\mu_x^2 + \\sigma_x^2 \\cdot \\delta[\\kappa],\n",
    "\\end{equation}\n",
    "\n",
    "and as correlated if this condition is not met. The samples of a signal which is uncorrelated show no dependencies between each other in a statistical sense."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example - Auto-Correlation Function of a Periodic Signal\n",
    "\n",
    "A periodic signal $x[k]$ can be expressed as\n",
    "\n",
    "\\begin{equation}\n",
    "x[k] = x_0[k] * \\sum_{n = - \\infty}^{\\infty} \\delta[k - nP]\n",
    "\\end{equation}\n",
    "\n",
    "where $x_0[k]$ denotes the signal of one period. The DTFT $X(\\mathrm{e}^{\\mathrm{j} \\Omega})$ of a periodic signal consists of a series of equidistant Dirac impulses (line spectrum). Lets assume that $x_0[k]$ is a wide-sense ergodic random signal. Expressing the ACF as convolution, transforming this into the frequency domain by the DTFT, and deploying the multiplication property of the Dirac delta, it can be concluded that its ACF is periodic with period $P$. The ACF is then given by convolution over only one period and by its periodic continuation, as\n",
    "\n",
    "\\begin{equation}\n",
    "\\varphi_{xx}[\\kappa] = \\frac{1}{N} \\left( x_0[\\kappa] * x_0[-\\kappa] \\right) * \\sum_{n = - \\infty}^{\\infty} \\delta[k - nP].\n",
    "\\end{equation}\n",
    "\n",
    "The ACF of a periodic signal is computed and plotted in the following."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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fafHixXrwwQfDvk99fb3q6+s9j2tqaiRJjY2NamxsjLD07UtjY5PP//neECtkDU4ha3AKWYNTyFpkrHxPSd8BO3jwoJqbm5Wfn++zPD8/X1VVVQGf8+GHH2rmzJl644031KGDua9g7ty5mjNnjt/yVatWKScnx3rB26H6ZskdudWrVyszPa7FQQoja3AKWYNTyBqcQtYiU1tba3rdpO+AublcLp/HhmH4LZOk5uZmXXfddZozZ47OOOMM068/a9YszZgxw/O4pqZGvXv3VllZmXJzcyMveDtS29Cku99aLUkaPXq08jplxblESFVkDU4ha3AKWYNTyFpk3FfHmWG5A/bSSy9ZfYrGjBmj7Oxsy88zo3v37kpPT/c723XgwAG/s2KSdOzYMW3atElbt27VtGnTJEktLS0yDEMdOnTQqlWrNHr0aL/nZWZmKjMz0295RkaGMjIybPo0qS3DONEhzsjowPeGmCFrcApZg1PIGpxC1iJj5Xuy3AH79re/bWl9l8ulDz/8UF/72tesvpUpHTt2VElJicrLy/Uf//EfnuXl5eW64oor/NbPzc3Vzp07fZYtWLBAq1ev1p///GcVFRXFpJwAAAAAENEliFVVVerRo4epdbt06RLJW1gyY8YM3XDDDRo6dKhKS0v1xBNPaM+ePZoyZYqk1ssH9+7dq2effVZpaWkqLi72eX6PHj2UlZXltxwAAAAA7GS5A3bTTTdZupzw+uuvj/k9Utdcc40OHTqk+++/X5WVlSouLtaKFSvUp08fSVJlZWXYOcEAAAAAINYsd8AWLVpkaf1wc3HZZerUqZo6dWrAvz3zzDMhnzt79mzNnj3b/kIBAAAAgJeoJmL+yU9+EvRvhmFE89IAAAAAkHKi6oC98MILevbZZ/2W//GPf+R+KgAAAABoI6oO2Msvv6xZs2Zp7dq1klo7ZGeffbauvfZaDRo0yJYCAgAAAECqiGoi5tNPP13Lli3T1Vdfrfz8fO3YsUPf/e53tWTJEn3961+3q4wAAAAAkBKi6oBt3LhR55xzjn7961/r5ptv1vr163X++efbVTYAAAAASClRdcAuuOACpaWlqV+/fsrMzNRPf/pT3XnnnRo8eLBOPfVUu8oIAAAAACkhqg7YkSNHtH37dp9/V111lerq6nTSSSfp0KFDdpUTAAAAAJJeVB2wvLw8XXjhhbrwwgs9y1paWvTee+9px44dURcOAAAAAFKJ5VEQd+zYoZaWluAvmJamQYMGaeLEiZKkd955R01NTZGXEAAAAABShOUO2DnnnGPp0sLS0lLt2bPH6tsAAAAAQMqxfAmiYRi69957lZOTY2r9hoYGy4UCAAAAgFRkuQN24YUX6v333ze9fmlpqbKzs62+DQAAAACkHMsdsNdffz0GxQAAAACA1Gf5HrBQHn/8cTtfDgAAAABSiq0dsI0bN+oHP/iBZ5TE999/XzfccIOdbwEAAAAASSuqecDaeuaZZzRv3jxdeuml6tq1qz788EPddddddr4FAAAAACQtWztgW7Zs0fr167V//3598MEHeu2119SnTx873wIAAAAAkpatlyBOnTpVkyZN0tatW7V06VJdccUVWr9+vZ1vAQAAAABJy9YzYG+++abn/8OGDdPf//53XXXVVdqwYYOdbwMAAAAASSmmoyD26tVLq1evtvMtAAAAACBpxXwUxFtvvdXOtwAAAACApMUoiAAAAADgEEZBBAAAAACHMAoiAAAAADiEURABAAAAwCFRdcBqamr085//XFu3blXnzp01YsQIXXnllerbt68kRkEEAAAAAG9RXYJ47bXX6qmnntIpp5yizp076+mnn9aAAQM0b948zzpZWVlRFxIAAAAAUoGlM2BLlizRtdde63m8bt06vfzyyxo5cqRn2caNG3X11VcrJydHU6ZMsa+kAAAAAJDkTJ0Bq6qq0pVXXqny8nKf5TfccIPGjx+vsrIy3X333Vq6dKm6du2q3/3ud/rv//7vmBQYAAAAAJKVqTNgTzzxhJqamvT000/7LC8pKdEll1yiLVu2aOvWrVqyZIn27t2rjh07qqmpSVOnTtVZZ52ls846SyNGjIjJBwAAAACAZGHqDNgdd9yhrl276jvf+Y7P8tWrV2vx4sX6yU9+ouXLl+vTTz/V559/rgULFkiSvvjiCz3xxBMqKyuzv+QAAAAAkGRMnQHr2rWrnn32WS1fvtxn+a9+9StdfPHFKi4u1i233KIhQ4aotrZWixYt0pAhQ/Tss89Kkpqbm+0vOQAAAAAkGUujIE6YMMHncX5+vt5++23ddNNN+uMf/6gJEybommuu0fHjx/W///u/nvXS09PtKS0AAAAAJLGoJ2LOzs7Wvffeq3vvvVd1dXVqampS586d7SgbAAAAAKSUqDtg3pjzCwAAAACCi2oiZgAAAACAeXTAAAAAAMAhdMAAAAAAwCF0wAAAAADAIXTAAAAAAMAhdMAAAAAAwCF0wAAAAADAIXTAAAAAAMAhdMAAAAAAwCF0wAAAAADAIXTAAAAAAMAhdMAAAAAAwCEp0wFbsGCBioqKlJWVpZKSEr3xxhtB133hhRc0ZswYnXLKKcrNzVVpaaleeeUVB0sLAAAAoD1KiQ7YsmXLNH36dN1zzz3aunWrRo4cqfHjx2vPnj0B11+7dq3GjBmjFStWaPPmzbrooos0YcIEbd261eGSAwAAAGhPUqIDNm/ePE2aNEmTJ0/WwIEDNX/+fPXu3VsLFy4MuP78+fN1991367zzzlP//v31i1/8Qv3799fy5csdLjkAAACA9qRDvAsQrYaGBm3evFkzZ870WV5WVqYNGzaYeo2WlhYdO3ZM3bp1C7pOfX296uvrPY9ramokSY2NjWpsbIyg5O1PY2OTz//53hArZA1OIWtwClmDU8haZKx8T0nfATt48KCam5uVn5/vszw/P19VVVWmXuPXv/61jh8/rquvvjroOnPnztWcOXP8lq9atUo5OTnWCt1O1TdL7sitXr1amelxLQ5SGFmDU8ganELW4BSyFpna2lrT6yZ9B8zN5XL5PDYMw29ZIEuWLNHs2bP1t7/9TT169Ai63qxZszRjxgzP45qaGvXu3VtlZWXKzc2NvODtSG1Dk+5+a7UkafTo0crrlBXnEiFVkTU4hazBKWQNTiFrkXFfHWdG0nfAunfvrvT0dL+zXQcOHPA7K9bWsmXLNGnSJP3pT3/SJZdcEnLdzMxMZWZm+i3PyMhQRkaG9YK3QxnGiQ5xRkYHvjfEDFmDU8ganELW4BSyFhkr31PSD8LRsWNHlZSUqLy83Gd5eXm5hg8fHvR5S5Ys0c0336znn39el112WayLCQAAAADJfwZMkmbMmKEbbrhBQ4cOVWlpqZ544gnt2bNHU6ZMkdR6+eDevXv17LPPSmrtfN1444367W9/q/PPP99z9iw7O1t5eXlx+xwAAAAAUltKdMCuueYaHTp0SPfff78qKytVXFysFStWqE+fPpKkyspKnznBHn/8cTU1Nen222/X7bff7ll+00036ZlnnnG6+AAAAADaiZTogEnS1KlTNXXq1IB/a9upev3112NfIAAAAABoI+nvAQMAAACAZEEHDAAAAAAcQgcMAAAAABxCBwwAAAAAHEIHDAAAAAAckjKjIAIAYFVzi6G3dh/WgWN16tElS8OKuik9zZXy7w0AiB86YDCNhgqcEmx725kDJ94DiW3lrkrNWV6hyuo6z7LCvCzdN2GQxgwqiGnWyiuqgr73uOLCqD8bEg/1GpxCey3x0QGDKTRU4JRgWbt8cKFe2l5pSw6ceA8ktpW7KnXb4i0y2iyvqq7TlMVb1DUnQ0drGz3L7cxa29f2fu/bFm/RwuvPJW8phnoNTqG9lhxchmG03f/AhJqaGuXl5am6ulq5ubnxLk5MBWuouCQZ8m9MBPux1TY0adDPXpEkbb93tPI6Zfu9j9mGiru6oKGSWoJlLZhgOQiVNbveA8mrucXQiIdX+9Q14TiRNff7FORlad2PR3PUOEVQr8EptNfiy0rfgEE4EFJzi6E5yysCVuruZW1/cO6juCt3VZp+H3el0bZBFOjH7P3ec5ZXqLmFYwipIFTWgrGaAyfeA4nvrd2HLXW+JGey5n6fyuo6vbX7sMVnIhFRr8EptNeSCx0whERDBU6JJGuStRw48R5IfAeOWc+A5EzW3CItIxIL9RqcQnstudABQ0g0VOCUaLejmec78R5IfD26ZEX1fCeyFm0ZkRio1+AU2mvJhQ4YQqKhAqdEux3NPN+J90DiG1bUTYV5WYr0DqtYZs2l1vsyhhV1i+j5SCzUa3AK7bXkQgcMIdFQgVMizZqVHDjxHkh86Wku3TdhkCRZykKss+Ze974JgxiAI0VQr8EptNeSCx0whERDBU6JJGtWc+DEeyA5jCsu1MLrz1WP3Eyf5V1zMiT558POrLkfd83O8FlekJfVLkYKa0+o1+AU2mvJhQ4YwqKhAqcEy1phXpa+f2GR8tssjyQHTrwHQmtuMbTxo0P627a92vjRobiNjDWuuFCvzhjlefzMLedp80/H6LEA+bAzawV5WXrs+nP1xo8v8nnvdT8eHdecJcp2STXUa3AK7bXkwUTMCS5RZhQfV1yoC07vrrNmr5LU2lgY2f8UlVdU6b6X3tH+mnrPugURTLrnrjSCvVag947nkZRE2S52SpTPFCxr6WkuTRvd35YcOPEedkmU7WKXUJOExmMH7f1dur/bUPmwKtRr1TY0+b13vCTadrFLovx+qNd8Jcp2sVOifCbaa74SZbu0RQcsgSXaDpGGSqtE2y52SLTPFChroZYn6ntEK9G2S7SCTRLqnosmkY6SOpG1RJFM28WKRPv9UK+1SrTtYodE+0y011ol2nbxxiWICSrYRHeRTJoXa+2xoZIM28WsVPxMqSDVtouZSUKZqNN5qbpdUu33kypScbsk02eivZY424UOWAJK1R1iskvF7ZKKnykVpOJ2CTd/DBN1xkcqbpdU/P2kglTcLqn4mVJBMmwXLkFMQFZ2iKX9TnauYO1cKm4Xs5/pmfW71b1LZkJdP51qvK9TP3isPuWyZnb+mPX/+jzhrtVPNd5Z+3D/F6aek0wTqFKvJY5Ur9dSsV2QCpJhu9ABS0A0VBJHqjdUzJb1gb+/6/l/olw/nUoCXaduRjJlzez8MY++9pHn/2TNfpFmLZkmUKVeSwztoV6jvZY4kq29RgcsAdFQSQztoaESSVmT/cb8RBNsAAQzkilr7vljqqrrTH9WsmavSLLmUuvoZsk0gSr1Wvy1l3qN9lpiSMb2GveAJaBIJrpLlJsKU0WwmzdDScaZ3iPJWqJcP50KQl2nHkoyZi2SSULJmn0iyVqyTqBKvRZf7aleo70Wf8naXqMDloBoqMRXe2qoRJI1KTlvzE9E4a5TDyRZsyYFnyQ0FLJmj0iylqwTqFKvxVd7qtdor8VXMrfX6IAlKBoq8dOeGipSZFlzS6Zr9RNRJN9fMmdNas3bqzNGeR5PGfU1U88ja9Gx+v09c8t5Wvfj0UmdM+q1+Ghv9RrttfhJ5vYaHbAERkMlPtpbQ0Xyz9qPx51p6nnJdK1+IrL6/aVC1iTf+WPO/5q5EajIWnSsfn+pMFAA9Vp8tMd6jfZafCRze40OWIKLdUOlucXQxo8O6W/b9mrjR4dS4nR4tJ+pPTZUJN+sXX9+n5DXtUdy/TRZ8xfu/gGXpILcLJ/1UyFr3kr6nETWTHA6a6mCes066rXI0F6zrj231xgFMYm4GyrBRhGzOlpVoFFjkn10Hjs+U7jR2lyS8nOzVFWTukeu3Ne137Z4i1ySz/cQ7vpp76Fg3UPulldUtausjRlU4PcdBPquzHzPsy4doB8u3WaqTIG+e6d2NpG+N1kLj6zZ895kLbxEzFoyor0WXntvr9EBiwOndh7e79O9U6bkkg5+Ua8eXbJ05HiDbn/ef4jYZB6KN9iwt+7P9LvrztFJnTIDfh/e24CGSiv3de33vfSO9tfUe5YXBKgg3e9TXlGlv27bp8PHGzx/65qToaO1jX6vn6pZm7J4i99n7tYpQ/8xpJcuGVTgtw3Cfc8XnnGK6TLFawcd7XsnQ9as/pa818/LzojoPSWyZvd7J0PW4iURsyYl5z6U9lpotNfogDnOqZ1HuDkR0lwKeLTAUGto5yyv0JhBBREFLx4NlVAj4biXTVuyVcHObrfdBjRUWo0rLtQFp3fXWbNXSWq9fnpk/1N8tme4rAVqpEipnbW2n/nw8UY9tf5jPbX+44DbINT3XNvQFLZM4XZmsdxB2/XeiZy18or9euj/3gv4WwpUF0Q6J01bZC02753IWZOo17wl8z6U9lrw16C9RgfMUU7tPMxMgBjqMlvv0XlK+5m7jtktXg0VMyPhhPrMgbYBDZVW3pVx28o5msk2pdTNWijBtkGo7zmUcDuzaHfQTr53omZt+tJtQX9L8ycO8VkerpzlFft1xZBept6XrMXuvRM1a9RrJ6TCPpT2mj/aa60YhCPG3DcYvrjlM/3kxV0he/xW5oQIVqlFOgFiIJGMzjN96Ta/H5Y7wOUV+32Wh5s8r+36dpfVW7BtEKuGiiFp5l92av2/Dtp2I22sshbq/ciadXbPARNuZ+beQT+zfrftWftN+fum3jvaoZbjnbVQv6W5K97zLDNTzrkr3jO9Hcha+8sa9VqrVNqH0l6LvqzeUqG9JnEGLKasHC2I5iiGt2iPYnnr0SXL8unmUEcnI2mofOvsnqZ+RHYMG2zXNpDMbYejXzbqP5/8py2nuMnaiWV2Zs29Q/a+PCPRsmZ2Z/bA39/Vk+t2O5o1t2h3uPHOWjCG5HNz95Y9R8OWs6om8HYna/7aY9ao11qxD7Umku1H1lo5nTU3OmAxEuklDNHuPOyYU8I9Os+R4w0a8fBqWyqIWDdUwo2EY4Ud36GV14j2FHcyZ01qveQhUbN2ybw1PteUF+Zl6d7LBiZU1qzszOKVtWh3uImatbYOflEffiUF/jxkzVcyZy3R96HJkDX2oeZ4j6aYiAeWyFpwXIIYA9GcVo5252HXkYXLBxfq9uftOd0cSLQNlWt//6Z+uHSbrv39mxrx8GqVV1TpvgmDoiqTmx3foZXXiObSjWTPmiR96+zEzZr3jkNqrXxvf36rLh9sz7XgdnyH4ebc8eZ01iKZVymQZMla986ZptYL9HlCZc2Oi17ImjntYR+aDFljH2qOodbRFMsrqjTi4dWettHNi96O+rXdUn0f6lTW2qIDFgORnlb23nm4z/L8fUelpdcYVtRNXXMiP/IhSXnZHfS3bZW23ccQiN0NldsWb5Ek/e66cxTNvd9pLumI11DDZvx9R6XfBILDirpZmtQ00vsXkj1rkvSXLXsTKmuh3sv9l5e2V+qRiYmRtfQ0l+69bJDpBoSTWXM3DrzveUjGrJmdUPbc07qG7aAU5Pr+9oLxztr0i/uHeMXwyJp5qboPTbassQ81p2tOhlpaZNv9WYGk+j7Uqay1xSWIMRDpKdHLBxcqPc0V9FpkM6NnvbKrKujwuGZVf9mk6i9DjxoT7HRz23kYvJd7T4bnbqiEOgVtpaHiHgHrV1cNDjl6TjgthjT1+S1aoHN06dk9g67nXaHd9ecdknyHKy2vqFJdU7Pl97eanWTPmiSfuXUCcTprmz85ErI87sp3/7G6hMjayl2VeuDvFZbf34mseTcukjlrkn/eAs0xE2pOGnmt7+4kmM1aU5RHWslaq/a8D022rLEPNedobaN++rfAA4a4Bbs/K95ZS5R9qFNZa4szYDFg9mhBW0+s3a25KyqCHsmYvnSbVu4KfoRlxY59mrZkS0TvHYlg4Wt7QMO7oeLmbqgEWl9e61ttqGz86FCYUpszbclWrQhyNGvlrkpNDzCpn/tMnHsbRlKxHjxWb+moKFkL/DiarH1+zNzlFp8crjW1Xjh2ZC2SI7hOZK26tjFsOZMha/MnDlGPXN/PX5CXpYXXn6sxg/J9lrvnpGm7vpv3+mazFriZZB1ZS/ysSfGt1xIpa+xDzTF7YCkQ9qHOZa0tOmA2W7mrUj/647aInmtI+v0bu0NWf8GuO125q1JTnw8+cV0sBLo8MFUaKu4jK21P3ZsZrjTcNgzlgb+/qxEPrw5Zcbsle9Zckrp1Mnf5hZNZO6WLuR1yn245ptYLJ5WzZraciZ61MYPy9eqMUZ7Hz9xyntb9eHTQm7DHFRf6rP/Y9ecGXM9s1kq/1l09unQ0tW4oZK397kPJmr9k34da4eSBJfah5tABs5F7JJ2qGrOdBX9mJ9zz5g6ZXU7K6RB2BB3v083e4t1QaTGkzpnpptY1w3soVin6CQTNcB+ZCfWjToWsGZJuOL+PuiZY1kr6nBS27N06ZahrTkeyZlKyZ02yPseM99+H9g2cKbNZO/BFvYb36x52XbPIWvvbh5I1X6mStS5Z5vZBTh5YYh9qDh0wm9g5oV44bY9kbP7kiK1DKh+pbVL1l6FPx3qfbm4rXg0VSVrw+kf6ot76tbzBeA/FKtk3HHYo7gwFO3qWKlnL6Ziu3/7jXzqaYFkzM+/c4eON+tGftpM1GyV61mLBbNbuXLZNf922z7b3JWvtbx9K1k5Ipawdqwu/D3L6wBL7UHPogNnkzX8fism8MoG0PZJh/vI8++RlZ+hv2/b6jSYTC80tRth7wJxi13DY4biPnr0Z4J62VMlabYO5itfprHkfsexh8sxrLJA1suYUspb6+1CydkJ7y9p3S3rp5R37yFqMhMpaKIyCGKW3/n1YGz79VMs2fWrL66W5JMMIPjKNe8K9eq8RW8xenhetBf95jqY+t1WSfOaYyA9yTbAdAo0wlOaK/rRxpMxM+BxqG1r1X3/YpInn9dboAfmSS/rHu/vJWowEypphnPh2TsrJ0BEbRuIzi6yRNaeQNbLmFLLmfIfk0dc+8vyfrPmyO2vf/rq5q7UkzoBF7Xv/+7aeXv+xjkd5GtX11b9bRxZ5HgfiPc+JW0mfk0xPjhmNFTurAi4/EMU11KGUV+wPOMKQU52vtnP8SL6jAQVa38w2tOJ4Q7OeWv+x/vOpf+o/n/wnWXM4a59/cWJ0qVjuOMgaWSNrZM1uZK39Zq00yCWHZO3E+rHI2h/e3GN6fTpgCcI98sysSwcFHWlm/sQhAW+ONDNEqB1eDjLMp3d/yM7T279Y8a4j12gHEmgoVrdxxYWaP3GI33Iz2zARkDV/ZC02yJo/shYbZM0fWYuNZMjaxiDDzpO1VomQtZTpgC1YsEBFRUXKyspSSUmJ3njjjZDrr1mzRiUlJcrKytLXvvY1PfbYYw6V1N/TNw31GXmm7Ugzbm2HBfUWbohQp9h5r9b+GB2pMSPYUKxubZe3HT0o2DaMN7IWGFmzH1kLjKzZj6wFRtbsR9YCI2vWpcQ9YMuWLdP06dO1YMECXXDBBXr88cc1fvx4VVRU6LTTTvNbf/fu3br00kt16623avHixVq/fr2mTp2qU045Rd/5znccL//5/U72O00dbBQZ9w2Onx3xn8BuXHGhLji9u86avSom5TSj7Q2mzS2GNn50SAeO1fkMyxtseSJ45pbzNLL/KUpPc6m2ocmz/O87KnXqSTkBRxMKNHqQk6OpmUXWyJpTyJozWevRJVMHTNzYT9ZakbXYI2utyFrsJXPWUqIDNm/ePE2aNEmTJ0+WJM2fP1+vvPKKFi5cqLlz5/qt/9hjj+m0007T/PnzJUkDBw7Upk2b9Ktf/SouHTCzyiv266H/e8/vGtvyiv26YkgvSfGvsNreYHrJvDUBj4yM/58N2u/waEBmGyreP07vif3u+vMOSVJhXpZmjvc/1W1GblYH1dSdqCQKcrP0nXN76XevfxTiWc4ja9Eha+aRtej8v7Fn6O4/7wy7Hlkja9GiXjOPrEWnPWQt6S9BbGho0ObNm1VWVuazvKysTBs2bAj4nI0bN/qtP3bsWG3atEmNjfbeJGhmRvnG5hbVNjSprrH1xtC2w3i6TV+6LeDQqdOXbtNL2/aqtqEp5kOMhjOwsIuamls8j4Odlg72Y16568RNyvm5mbZeIz3ton6m1qttaFJtQ5P+b+c+TV+6ze/vVdV1fsv/+e9DniGFv2xoVm1DkxqaWvye6/1jlqQVd4zQjcP7mP4MoZjJmrts7py4j2y1FSxrP1y6TX/b9pknq/E0sLCLz+Nos2anO0abz1p9U7NW7qo0nbW3dh/2ZO1YXaNqG5rUEuB33zZrL027wLasmfm+vOs0qTVr6z486LfeD8NkrbHZ/3cUiJn8R+rsXnk+jxMpayP7m5s01/27jyRr6z48qGN1jUF/922z9rdpw3XzBX1NlSscs1nzzkljU4ve+OBzv/XCZS0RnHtaV5/HVrP2yjuxy9qMMf1NrefOSais/TBI1ta8/7mO1TX6tCO8BcrapK8GUoiW2ay1fWw1ay9v3xt5IW3Udn5Vq1l79d0THR6761+zWXPnZOWuSr9MScGz9uLWz/Taewd0rC54mz9Q1qZ809y+3YykPwN28OBBNTc3Kz/f9xrP/Px8VVUFHnGoqqoq4PpNTU06ePCgCgv9b5ysr69Xff2JENbU1JgqX59uOTpwrCHkOj/76079bXuVJpxdoLGD8vXgivcCzs4eqmt157Jtajak5yYNDVum9DRXzDpq3/jFaj185dcjfv5P//qO5/93l/XX//vzLjuKJUmabXL2+aEP/kOSlN+lY8Dv3JD/zbO3PLPJ8/9OHdN1vKFZ1wztFfa9fva3nXp55/6w65lxTcmpeuT1f4dcZ+z8tTr4RYOWTj5PB79oiChrP1y6XcU9d5vKWiyNm/+G/nHniIif3zZrP7Ixa/9494Cp9YY++A9ddW4vvfGvg6az5j18teurIXT/8v1hYd9r7Py1to1CNX10P836a+jf09AH/6EBBV20/PZSvfLO/qBZC+WHS7freF2TLjsr+P0UbuHq2Wg8sfZf+q8oGnmxzNrKnYEHdmhr6IP/0ItTztfsl96JKGuSdPopnfSXKd8I+17f+MVqfb3NAZJImc3ag1cM0jVDT9Ur7+zXfcsrdOi4taxPX7pdYwf2UGNTfA8uHTr2ZVSXed2//F3P/+3OWpfMdFPrfW/R21p667CQWWurbda+N7yPfnhx+MbuN36xWvdfPtBUucIxk7VhP/+H3r+/9QD+K+/s191/2anaRnMHidx+/JedumTAKaaylp2Rpi8tvr5ZLc1NamyMvC340Ir3Pf8f9/V8PfumPcP7S+az9vL2vbrynF6a/dI7Af8eLmsul/TINYM1sv/JYd9r5MOv6e2fXGSqXGa4DO9B+pPQvn371KtXL23YsEGlpaWe5T//+c/1hz/8Qe+9957fc8444wzdcsstmjVrlmfZ+vXrNWLECFVWVqqgoMDvObNnz9acOXP8lvee/kelZeb4Lc9MN1Tf7L07C7R7C7Xc6jon/HJYkzLTpU2fu/SHf6XrjLwWlfUyVNMoZadLj7/XGuzRPZu1ep+5kJvRt7Ohj7+w55zVgyVN+unm2BwfeOi8Jn123KXyvS69X52msb1adOlpLapvlu5+KxbvGX7bn3Nyi7YeiuyEtEuGDMU3a/N3pWv3MZe+d0azcjpINY3SkTpp+aet+bq2X7OWfGRf1uzkRNYerWj97A+UNCm3o6LIWrjtE37bTxnQpMfei/zznpJl6PM693s4m7XP66T/3tFBeRmG7h96ovHy5Htp2nmk9ffTXrP2y2FNeutzl/68O11DurXoljNbG23xzFq0n/eC/Bat3++uF53N2osfp2njgTRd1rtZl/Qy9FGNSwe+lP64+0S22mvWHjqvSb/cka7D9S59u0+zRhUaSnNJmw+69OyHVr8PdxM0nlkzdMPpLfrDv9I9jyMfo9Dac+cObdKsTa3lnntek7LSpY9qXFpb5dKOwyfaBHZn7etdW/TOUXsugotl1m49s1m/fz9deR1bt1G/3NasPfpOmj6ssVr+aLJ2QqjP21Jfq0/nX63q6mrl5uaGfJ2kPwPWvXt3paen+53tOnDggN9ZLreCgoKA63fo0EEnnxy4Fzxr1izNmDHD87impka9e/f2WScvq4Oqvzplufaub6rFkEofXvPVX4NtUDM/VGsVwdixZcrp2EFlzS36f80tSnO5lJXR+sOtbWjS4w+sliRNvKhEq5/bZum1Q1n0XyN10bx1trzWxZdcrJ9uXuN5PHlEHz257hNbXnv8uNbvZ0pTi5pbWtQhLU0dO6SptqFJd7+12pb38BV+28+/eZRG/bp15M7fXTtYty/ZHvIVu2Zn6OiXrUd41909SmkuV1yzNnpMs1oMQx3T09QhvbVSPFbXqOU/f02SdPHwoVry0VZTr+lS+EkRV985QqN/kzxZu/Wry1ayM9LlcrmiyFq47RN+218/YbQee2+tJOl/rjlbdyzbEfIVvbO2/q4L1SHdpW88FJ+sZXZI1/VXNMsll7I7nmiMlH6zXsPmtpYpmbL2XyP76ok3PrbltceOLdO30tN0b3OL0l0uZXrV+fHKmvfn/c1VZ+nOP4W+V61t1rI6pqnk56+bfj/rZQ1s7NgyXZqW5rN/kFonlb3zeIOnrk2mrE25sK8eW/uxLa89flyZLh3Xeugvs0O65x6cEXUNetazvcyKZvsFztq8q4o140+hz/z5Zm2UOmd10B8ecP9OojmQbO2548eN0aXjW5/j3j9I0m1NLaqpa4xZ1n43aZS++evQo4Wb1TZrt40q0sI1u2157du+e4mmpbn86vzzR9V77YfMsqeusJq1YJL+HrCOHTuqpKRE5eXlPsvLy8s1fPjwgM8pLS31W3/VqlUaOnSoMjICn/rPzMxUbm6uzz9JWnj9uSdeY8aFnv93yclSXqcsv9dxQlp6B2VkZCg7K1N5nbLVJSdLGRkZnn9upf17mJ4QsO210W0nvJOkLjn2XW+ekeF7bGBG2QA9dv25KswL/p2GqqK9y+v+Hjpnt34/nbIz/b4bp3XKPnH99Df6hb+nY+alZ3r+f1Ln7LhnrTXv2crOOvFdZmV6f6ZTTGet7dC8gbKW2ym5spbXKVt5nbLVsWPHuGctK/PEew/vf4rn/11zApfplTtHev5/UpfW+iQe3JnK65St3E6+dVrn7BNlSqasTR9zpq1Zy/mqzu8cpM53mvfnHXlmD8//zWYtOzM+w3SnpXcIuH/o2LGjT12bTFm74xJ7s5bbqbXOz8o8UafFa3u1lunE573wzPCXLPvsQ7tkx+13kt4h8P6hU3ZmTLPWOdu+e7baZu0HF59hW9aC1fnx2g9JwbP2zC3n6eHvnGX6dZL+DJgkzZgxQzfccIOGDh2q0tJSPfHEE9qzZ4+mTJkiqfXs1d69e/Xss89KkqZMmaJHH31UM2bM0K233qqNGzfqqaee0pIlSyy/t/dNjPEe0cbtknlrNOfyrwecBNCbe0LA2xZvCXvE5NUZo7Rrb40OHKtTjy5ZKu6V6zd8qvd9ZZ0y06OabX7Tx/7zU4wrLtSYQQV6a/dhz3Coba8bb/s53Ftk1qUDAt6gmYjM3J/3m/IPHShJeGTN97GUXFnzdjTI/WFrAtxgHg9m71sla4kv0bNGveb7WEqurLEPJWvxMKyom5oKzXcMk/4MmCRdc801mj9/vu6//34NGTJEa9eu1YoVK9SnT+uIX5WVldqzZ49n/aKiIq1YsUKvv/66hgwZogceeED/8z//E9Mh6J3smh2oqddti7do5a7wN2e7JwQsCHGkQmr98Zf2O1lXDOml0gDzYEjShEfWe/4fzY9ZkqYs3hK2HG3nd5g/cYjf5wg3QZ837yFMnRAsE1v3HA373FCTHpI1a9pz1sw0VH696gPLrxsLl8xbYypnElmLp1TIGvXaCclYr7EPJWt2i0UmUuIMmCRNnTpVU6dODfi3Z555xm/ZqFGjtGVL4NDYxXuH476tz4kRT9zvNWd5hcYMKgh7Zs7MkQozzMzZEEtjBuXrW2f39HyOHl2yPHNEtB06tq3mFkO/WPFuyHXays/N1IGa+oi2aagtcvAL698jWXNWqmQt2oaK+/WdyJq7obLw+nPDHi2WyJqb1YYKWaNeS5Z6zft53mdhItmHhnv9WCFryZ21aKTEGbBEVF6xX5fM871B0BVhFzrQ08rCHCEwJFVW1wWcTyyQUEcqAnF6vrE3Pzpk6j3NHPkJ5K3dh8Pu/Nv6yaWtQ99GslkL8rI07+rBnsfeP+juna1dR0/W7NWeshZtZ//2i/opP8D9BWYE+izXn39a0Oy633XO8gpLlyO256yZaajkZPiOrNZeska9Fliy1Gt5ORnq6jVcv/dZGKv7UIms2ak9ZS0adMBiZPrSbX4Bcefx0mJrl40EqghWmTyqeeCY70SA3j+Kt3YfjuiHuXJXpV+DP9a+97+bNOLh1aYvQWor3Odu+z2ZMWZQvqnLAdq697KBuveyQXpo5YkpErx/0Oe0mYgzEO9BUUJl7ZbhfdStk/mbbcla6mSta3aGnpv8jZBZi7az/+hrH0kydOcl/fWbqwdHnbXFb+5RqIlRgjVUyFrgz22moVLbZnLl9pI16jVrEqlem35xf1XXNnpGMWzr6Jfh5wT03oeGytq0i6xNvEvWUidrkvTdc3uFzNrq98zN+RkIHbAYCfYzcUna8JG5oxw3lvbRklvPV7nX6IpW9ehyImxtf4g3L3rb8o9k5a5K3bZ4i+WjD3aoqq4zfa20NzOf2/t7smJccaHW/Xi0ltx6vq4b1jv8EyTtPfqlbn8++HfofSN6sKM1Pyo7w/P/UFn72/Z9Onw8/M5o2kWnkzUviZ61KRd+Lez6R79s1KaPj4TMmtWGSqDO/v6aes1/9UPtOVzrWNa8d8BkrVWgzx1JQ0Uia96o1xKvXnv2zU9CXkrmPcCGmX1oqKx92WDu/ijaa74SPWtm22uvvnsgZNZC3bcaDh0whxlS0J50W+OLCy2dlm2rMC/Lc3o62A/Ryo+kucXQnOUVEV1De+9lA/XbiUP07M0lun1gs+ZddZaeueU8S68RySVIZj/3sKJuOinI0MjhuE+jXzLQ3JnNv27bZ/oH3XY4WbfRA3oEXO7NkHT4uLms9c/vTNa8JHrW+vXobGr9Ret329pQCfRa7mWL1n9sqkzRZk06sQMma6E/d6QNFYmsSdRrUmLWa+E6395lNbMPDZW1F7ftNVWmsYMKyJqXRM9a2dcLTK0frr0eTeeWDlicdM3OCHkt6kk5GT5D3EfivgmDlJ7mCvlDtPIjeWv3YVVWWz+iWpCbpZsvKPJc53tGV0MTzi70uXbZbJVl5VppK587Pc2lCYN7miyFv5W7KjXzhdAT2rokdeuUYWnn8eqMUVpy6/n67cQhlitAK7pHOf8MWXMua5J0ssnLr6zsPKLt7Js9sBRt1twNFbIW+HWkE597WFE35WZHN9ZWe84a9Vpi1mtWRLMPdR/E7NapY9jv90d/2h7xJXcSWXM6a0N6dw35d5fkc99XLNABi5NbLiiSFDzIR2obNeq/X4v4B33nJWd4RgoL90M0+yOJ9HKWWZcOMHVUyMpxIzNlsfq5zez8A3EftTlwLHjHyv3Z/mNIL0uvbfVm20BivfMga85lTTLf2be687Cjsx/uwJJkX0OFrAXm/bnT01y68fw+Fkrgqz1njXotMeu1bp2sZc2Ofei3h/T0vH8w+2taz9JEMjw6WXM+a2Pnrw36d/dnu+WCvhG/hxl0wGIkWDhdaj2CO2306WFvCHSfdg30gw4V/vwumZo2+nTPY7M/xHDrRXo5i5k5HQLNCRFtWax+7nBnHAN952ZP87vnt7hkkLnT3laEy9qDVxSHXE8KvfMga4mRNclaZ9/qzsOOhkq4A0tS5FlLc0kLrjsxBD1ZM7fe90eFHkSArPmjXmuViPXag1cUqzAvK/T2C3KGNVJjBhVo4fXnhnxddxtg7or3/P5G1hIva6EuHXS316aN7h/TrNEBi6G2G8392H0Ed1xxodbcdVHQa1lD/aADvb7bTy4b6HMEw+wPMdx6w4q6hQ1jt04Z+s011o9qjhmUr3U/Hq3nJn0j5NFUd6fCzE7b6uf2/s6Cbbu2zJ7m/9V3B2tccaGp7zCSH3SorF16dmFUO49Ar+9G1lo5kTWrnf1Y7DzMHliKRdZ+fdVgXXr2ifm/yJq59UIdzSZrgVGvtUrEeu3Ss3vqvgmDQr6m972EZoTL2rCibhpXXKhfXz0k5OsYkqpqArcHyFpoiZK1bp0ytOauizSuuFDpaS7bs+aNDliMhJrl23sS0c2fHNGR2uDXswf7QYc6AtH2CEa4H6LZH0m4MLok/eI/ztJ/nBPZUc30NJcu6N9dD33nrKCvL53owIYTzedue49CQV6W5k8c4ree2aM2B4+3Hm2JxQ/aTNai2XmQtcTImtXOfqx2HmYOLMUia2OLfc8ek7XAQn3utp0Vska9Fkoi1mtS6/4s1BVEkVyeFi5rUuQTPJO15Mna4eON2vzJifkLY5E1t+juzkVQoWb59hbpdbptXz/UbOjuH+Jti7fIJd8Rf6z+SNxhnLO8wi/I8ycO8elcRmpccaHmTxyiHy7d5rO8IC9L900YZPo9ovncr84YpV17a3y2XX2T73C0b+0+bHpuG++jO6G+Q8n6D9ps1iLdeZC18JzIWqgDNd7cnX3J/qzNnzhED/3fez6vFei7ImuB3yMZsiZZP7AkkTWy5iuW9ZrU+hnHDCowtf3CMZu1aC7rI2uhJVLW2tZ/dmbNGx2wKHmPRLPp4yM+f3Nf5x7KxwePR/S+5RX7PaPUSFJtQ1PI9YP9EK3+SNyv5Q7jZ0dqddefW2+cNXPtsFner/Xf3z1bp56UE7BTYaaskXzuQNuu7X0ENy96WwW5meqak6Hq2sagp7W75mT4HbUJ9YNuOwnhyP6neEZHciNr7S9rZm8+b9tIiCRrwZjt7EeaNcn3+yBrwctqV9baivTAkrtcVhsqweo1s1mLtFFMvWa+rIlYr7V9D+/tZ3UfajZrR47XK80lhRqAMNDfyZr5siZ71gbnm7/Umg5YlK54dJ3cX+OUxVssPXflrkr95tUPw68YwPSl25TZIS3iH2KoSsYMdxhrG/I8P+hYuezsQuV0jDyqdnzulbsqNb3NER6pdWjlcNeuH61tVHlFld+2CvaDnvDIes//b170tgrzsnT54EL9dds+z3KyFhuJnDUzc7oF6uxL1rJ234RBuuD07p7lVjv7ZrMWqqFiBVmL7nOHOrB0NMwR4yMBptSw0igur6jSfS+941netl4z02E00ygOhHrNvHjXa1LgrAUTyT7UTL12+/Nbw+7vA+WQrJmX7Fk7JdPcxN0SHbCoHTjWoLRM/68xXEPCfTNgNOYsr9CYQQWWgmlmh5aKovncZuancLkkI0jN7JK1bXXgmO+lFpXVdXp87e6g65O1xBKrrJkRrLMfTNusVVXXacriLT43Vlvp7FvJml0NFYmsRSqaA0uS9MDfKzS22Fy90LahEq6DZ6YzbrZRHAz1mnnxrNcka1mL1T40mvKTNfOSOWsHLEzMzCAcMTJ3xXshJ8qLdJI8NysT3CE6ZrZVsM6XZG5bmZ0pPhCyljqi3Vbuzn6oPIT6m/svwSa6DTfHTbTll8xNMoromTmwFI6VeqFtQyXc2bVw9Vq0DS3qNefYUS+wD4UZ8c6alRTSAYuRqprQGzDSwTeCvU7byztowNjH7m0ViPeoO1Y5nTXETrTfsZkdfTRZC9dQcaL8sIcdDRUp9DaPZj8Url5zovywB/tQe18Hwdu8iZ41b3TAYijUBoz0xuG2Pj5Yq5W7KnXJvDWeZTcvelsjHl6tlbsqbXmP9iLYD9qubRXqdT4/Zv60dSBOZU2is2+HWGctVB6iyVq4hord5Sdr0Yt1QyXUNo+2oRKqjHaVn3rNPuxDQyNr9gjV5k2GrLlxD1gMhdqA7jkPqqrrgp6yTPvqvqJQP83fvPpBwOVV1XW6bfEWv3nHENjKXZU+N4N7D0jQYqJyDLWtXGodxSfUXBundIl8NnXJmazNf/UD1TY0+tzI7P09kTNzos2aGaHyEG3WQjVUzGTNDPeBpWDfE1kzJ9R3GG1DxUy9Fm1DJVQZ7WpoUa/Zg30o+1AnrNxVqdsWb/H7nt1t3skj+4Z9jXhnzVMOW14FfgpyQ2/AUJPkub76d+vIoqiub5e4n8IM9w96f03gAQl+8tddYV9j0ogiSeYmcwykpM9JVorsw6msGZIeX7s74Pd02+ItnHE1wY6sdc3JiGqSzmiyJoVuqITLmhS6/G6/efUDTQnyPZE1c0Jl7bbFW7T6vaqwr+HeVpHWa9E0VMLVa2Ymbu2aE37Yaeq16LEPZR/qhHD3rRqSnlr3cdjXiWfWvNEBi1KwTTTr0gFhR1AJNsN2QV6WFl5/rmZdOkh3XtI/4rI5cT9FrE6lO3WK3syN6OFuFpek0QPyQ27LcEe2vLNidZDZeGfNqc4+WWt1y/Dodh7RZC1cQ0UKnbXHrj9XD115FgeWYsyuhsovvn1WVPVaNA2VcPWamc7+Q1eeRb1m8+sGeh/2oexDY/G6bZm579PMW8cya1ayxyWIUeqRm6nPA1xlYXaSu3BzHvTt3inqMsbqxs9QlxxceMYpMXldu0/R23kj9xVDetkyb0eP3EyfI2TuOUxe2l4ZsKyJkDXvzn4shs0layf07Z5j2ySdbbPmHhrcpcCXZ5hpqEjhs3bnJf0jnpcu1lmTrE9QHe/XbcuuhspJnTqqtN/JEddrbRsq3m/pfhxsOHoz9ZqZiVvrm1rCvk4w1GvhsQ9lH+pU1uwcYCNWWeuRm6k9Jp9LByxKq+4cpfcONenAsTrlZWfo5kVvW36NUHMe2HGdu9XXMHP0Itx1uPMnDrH0nmZfN9TRiUgaNHbfiG7HvB2vzhilXXtr/CqFu8cN9FQWiZo1q98nWbOuR5esqBrF3gJlrbyiyq9B62a2oSKFzhoHlpKnoSLZU6+1bai4O0neOY6kXgvXKKZe833dRK7XJPahZC04uwfYiEXWBpzcQd3uN/dcOmBR8t6AtQ1Ntr9+NDe1m7mZsK22jQQ374kKw11y4FLrcNVWmXld78kM285JFEmDxokb0a0KVikkctbcrHyfZM2atlmzY+cR6DXaNmgjbaiEwoEl39dN9IaKHYI1iiVFXa+F+i1Qr/m+bqLXa3ZgH5qaWYt2MBQnslZTU2P6udwDluDMXOce6m/h7gfxFuxGWkn64dJtWrGjdeSecJccGGodrtoqM6/rPkW/clelpi/d5reO1ZtZzd7IHc2N6MkiVNbCMTP4gzey5i+RsubeqVwxpJetOyu3cN9FKFazJvkPW+zm3Sgwcy9LLBoqku+9H4EaKlanFTHz/aa5gv/OI/mOw/HOVGm/kx2rM6nXfF+3PddrsUbWfF/X7qyZHQwl2N+lxMoaHbAkEO6m9seiuJnQLVQjwW3akq1asaMyZpf+mH3dquovNfOFnaYbNKGYvZE7mhs2k0mwrBXmZen7FxbZshMla2SNA0u+r0tDJbao13xRr8UOWfNlZ9Ykc4OhJEvWuAQxSYS7zj3a+0HM3rQ99fktUY3MGIrZU+/r/3Uo5KhKVm9mNXMjtxT9d5wsQmXtnNNOinrwB7JG1qTw34WkqLNmtqHyqFxqbIl8sIZQrDRU5rxs/pKecMxkzY7fc7KgXjuBei22yNoJdmdNCt8eDvf3REEHzEaxHuEq1HXu0d4PYuUoyZK39qggN0v7awJfh+uSlJ+bZflocbjre1tfN1Pl7+4P8Fd/Vj6TmR+sHffcBGM1O/HKmh0VG1mLb9YSCQeWTqChEnvUa6lbr7EPDSwVsyaFz1IiZS0YLkG0Sdt7DCK5bj+erNz4WVVTr2uHnSYp+Kn0WZcOsFwGM5cyXDvsNFV/GX5OEcn6zcHxukfBanbinbVovyeyFr+sSdbnbIn1HC+hvotov6dIGiqh7mUpyLU+4ICZe2QKHGioBPsOY5nFRMtaKNRr/pKlXmMfGlyqZi1e7MwOHTAbhJoFPllmN3c3Esxyz0UU7DpbK8NVewt3fa/Z4au75mTEZPAAu1nNDlk7gaxZl2wNlWjRUImf9pY16rX4YB8aHlmzh93Z4RLEKFkdijNRuRsJUxZvMbV+uLmIohniNdQp+o0fHTL1GrcML0ro71uynh2yRtaiYXUo9GiGTk8U7oaK2Yliw01yHek8YOHukTE7WXCyNVTaU9ao15zHPpSsOcVsdlbcNtT0a9IBi9Lmj4+YHuEq0e/pGFdcqAXXnaNpS7Yq2JUfLtk/F1EgwV7XzDwQXXMyNG306baXyW5WRkcr7Xey5fUTGVlzFg0VGipOaa9Zk6jXnMY+lKw5xWx2Nn98xPRrcglilD7/wtyR1VgNBWq3S8/uqUevPTfg3xJheGIz82w8dOVZCb+jlsxnwr2e1fUTHVlzjpWGRyTrJzJ3QyXUZnLJdw6eWN3LEux1zczblWoNlVTMmkS95iT2oWTNKWYzYbZPINEBi9opnc1dh5ss1+1L0qVnF+qx68/1u8Y4UeZRCDXPxmMJUD6zzGbCvZ7V9ZMBWXMGDRUaKk5p71mTqNecwj6UrDnFbCbM9gkkLkGMWknfk8IOxel9CjhZJPrwxIlePjPMDOPqnR2r6yeLRN+WiV4+M2iofNVQSQs/V1G8BLtPrDBBymcWWWuV6PVGopfPDPahrRJ9WyZ6+cwwm52SvieZfk06YFFyH7m8bfEWuSSfDZMIR1ajkehzESV6+cKxmh2yFj+JXr5waKi0SvSGQKKXzwyydkKi1xuJXr5w2IeekOjbMtHLF04sssMliDYINxRnshy5hPOsZoesIRJmhkIP1FAxu34yieccbGYkevnCIWtwEvtQOMXu7HAGzCapcOQS8WE1O2QNkQg3FHqwhkqiXrKHxEXW4CT2oXCKndmhA2ajZD/Fivixmh2yhkjQUIFTyBqcxD4UTrErO3TAAKAdoaECp5A1AAiMe8AAAAAAwCF0wAAAAADAIXTAEBPNLScG6Xxr92Gfx1bWAQAAQGzQXosPOmCw3cpdlbpk3hrP45sXva0RD6/Wyl2VnmWvvLM/7DqAGew84BSyBqeQNTiB9lr8uAzD4BcbgZqaGuXl5am6ulq5ubnxLk7CWLmrUrct3uI3oaZ7HKtHJg7Wli1btOiD9KDrMBcHzFq5q1L3vfSO9tfUe5YVfjV09cVndteKFSuU3qdED6x4L+A65AxmkTU4hazBCbTX7Gelb0AHLEJ0wPw1txga8fBqn3lcvLkk5ed21Jd19apuCDy0sEutc7+s+/Fohh9GSOw84BSyBqeQNTiB9lpsWOkbcAkibPPW7sNBf8ySZEiqqmkI+mN2r1NZXae3dh+2v4BIGc0thuYsr/BrgEjyLHtwxbv6y8dpIdeZs7yCy3YQElmDU8ganEJ7Lf7ogME2B44F/zHH87WQeth5wClkDU4ha3AK7bX4owMG2/TokpWQr4XUw84DTiFrcApZg1Nor8Vf0nfAjhw5ohtuuEF5eXnKy8vTDTfcoKNHjwZdv7GxUT/+8Y911llnqVOnTurZs6duvPFG7du3z7lCp6hhRd1UmJelYMfmXJIKcjsqr6MRcp3CvCwNK+oWm0IiJbDzgFPIGpxC1uAU2mvxl/QdsOuuu07btm3TypUrtXLlSm3btk033HBD0PVra2u1ZcsW3XvvvdqyZYteeOEFffDBB7r88ssdLHVqSk9z6b4JgyTJ7wfrfvzTSwfqO31bQq5z34RB3NCJkNh5wClkDU4ha3AK7bX4S+oO2LvvvquVK1fqySefVGlpqUpLS/X73/9eL7/8st5///2Az8nLy1N5ebmuvvpqnXnmmTr//PP1yCOPaPPmzdqzZ4/DnyD1jCsu1MLrz1VBnu/Rt4K8LC28/lyN/Xq+Bp9s6JGJg4Ouw+hNCIedB5xC1uAUsgYn0V6Lrw7xLkA0Nm7cqLy8PH3jG9/wLDv//POVl5enDRs26MwzzzT1OtXV1XK5XOratWvQderr61Vff2K+jZqaGkmtlzQ2NjZG9gFS1MVndtc3+4/Upk+O6MCxevXokqmhfU5SeprL812NPqObLhkYeh0glIvP7K5HJg7WgyveU5XXXDgFeZm6Z/wAjT6jm5o/MTT/qmLNfeXDgOtcfGZ38oawyBqcQtbgJNpr9rLyfST1PGC/+MUv9Mwzz+iDDz7wWX7GGWfolltu0axZs8K+Rl1dnUaMGKEBAwZo8eLFQdebPXu25syZ47f8ySefVE5OjvXCA7BFiyHtPubSsUapS4ZU1MVQ24O/ZtYBwiFrcApZA5JPbW2tJk+erKNHjyovLy/kugl5BixYZ8fb22+/LUlyufxrG8MwAi5vq7GxURMnTlRLS4sWLFgQct1Zs2ZpxowZnsd79+7VoEGDNHny5LDvAwAAACD1HTt2LDk7YNOmTdPEiRNDrtO3b1/t2LFD+/fv9/vb559/rvz8/JDPb2xs1NVXX63du3dr9erVYWeszszMVGZmpudx586d9emnn6pLly6mOntoVVNTo969e+vTTz8N+50D0SBrcApZg1PIGpxC1qwzDEPHjh1Tz549w66bkB2w7t27q3v37mHXKy0tVXV1td566y0NGzZMkvTPf/5T1dXVGj58eNDnuTtfH374oV577TWdfPLJlsuYlpamU0891fLz0Co3N5cfNBxB1uAUsgankDU4haxZE+7Ml1tSj4I4cOBAjRs3TrfeeqvefPNNvfnmm7r11lv1rW99y2cAjgEDBujFF1+UJDU1Nem73/2uNm3apOeee07Nzc2qqqpSVVWVGhoa4vVRAAAAALQDSd0Bk6TnnntOZ511lsrKylRWVqazzz5bf/jDH3zWef/991VdXS1J+uyzz/TSSy/ps88+05AhQ1RYWOj5t2HDhnh8BAAAAADtREJegmhFt27dQo5eKLVek+nWt29fJfHAj0kvMzNT9913n8/9dEAskDU4hazBKWQNTiFrsZXUw9ADAAAAQDJJ+ksQAQAAACBZ0AEDAAAAAIfQAQMAAAAAh9ABAwAAAACH0AGD7T7++GNNmjRJRUVFys7OVr9+/XTffff5zbO2Z88eTZgwQZ06dVL37t11xx13+K2zc+dOjRo1StnZ2erVq5fuv/9+RrGEj5///OcaPny4cnJy1LVr14DrkDXEyoIFC1RUVKSsrCyVlJTojTfeiHeRkGTWrl2rCRMmqGfPnnK5XPrrX//q83fDMDR79mz17NlT2dnZ+uY3v6l33nnHZ536+nr94Ac/UPfu3dWpUyddfvnl+uyzzxz8FEh0c+fO1XnnnacuXbqoR48e+va3v63333/fZx2y5hw6YLDde++9p5aWFj3++ON655139Jvf/EaPPfaYfvKTn3jWaW5u1mWXXabjx49r3bp1Wrp0qf7yl7/oRz/6kWedmpoajRkzRj179tTbb7+tRx55RL/61a80b968eHwsJKiGhgZdddVVuu222wL+nawhVpYtW6bp06frnnvu0datWzVy5EiNHz9ee/bsiXfRkESOHz+uwYMH69FHHw3491/+8peaN2+eHn30Ub399tsqKCjQmDFjdOzYMc8606dP14svvqilS5dq3bp1+uKLL/Stb31Lzc3NTn0MJLg1a9bo9ttv15tvvqny8nI1NTWprKxMx48f96xD1hxkAA745S9/aRQVFXker1ixwkhLSzP27t3rWbZkyRIjMzPTqK6uNgzDMBYsWGDk5eUZdXV1nnXmzp1r9OzZ02hpaXGu8EgKixYtMvLy8vyWkzXEyrBhw4wpU6b4LBswYIAxc+bMOJUIyU6S8eKLL3oet7S0GAUFBcZDDz3kWVZXV2fk5eUZjz32mGEYhnH06FEjIyPDWLp0qWedvXv3GmlpacbKlSsdKzuSy4EDBwxJxpo1awzDIGtO4wwYHFFdXa1u3bp5Hm/cuFHFxcXq2bOnZ9nYsWNVX1+vzZs3e9YZNWqUzySAY8eO1b59+/Txxx87VnYkN7KGWGhoaNDmzZtVVlbms7ysrEwbNmyIU6mQanbv3q2qqiqfnGVmZmrUqFGenG3evFmNjY0+6/Ts2VPFxcVkEUFVV1dLkqdtRtacRQcMMffRRx/pkUce0ZQpUzzLqqqqlJ+f77PeSSedpI4dO6qqqiroOu7H7nWAcMgaYuHgwYNqbm4OmBsyA7u4sxQqZ1VVVerYsaNOOumkoOsA3gzD0IwZMzRixAgVFxdLImtOowMG02bPni2XyxXy36ZNm3yes2/fPo0bN05XXXWVJk+e7PM3l8vl9x6GYfgsb7uO8dWgCIGei9QRSdZCIWuIlUC5ITOwWyQ5I4sIZtq0adqxY4eWLFni9zey5owO8S4Akse0adM0ceLEkOv07dvX8/99+/bpoosuUmlpqZ544gmf9QoKCvTPf/7TZ9mRI0fU2NjoOfpSUFDgd0TlwIEDkvyP0CC1WM1aKGQNsdC9e3elp6cHzA2ZgV0KCgoktZ55KCws9Cz3zllBQYEaGhp05MgRnzMTBw4c0PDhw50tMBLeD37wA7300ktau3atTj31VM9ysuYszoDBtO7du2vAgAEh/2VlZUmS9u7dq29+85s699xztWjRIqWl+UattLRUu3btUmVlpWfZqlWrlJmZqZKSEs86a9eu9RkufNWqVerZs6fpxjeSk5WshUPWEAsdO3ZUSUmJysvLfZaXl5fTEIFtioqKVFBQ4JOzhoYGrVmzxpOzkpISZWRk+KxTWVmpXbt2kUV4GIahadOm6YUXXtDq1atVVFTk83ey5rA4Df6BFLZ3717j9NNPN0aPHm189tlnRmVlpeefW1NTk1FcXGxcfPHFxpYtW4xXX33VOPXUU41p06Z51jl69KiRn59vXHvttcbOnTuNF154wcjNzTV+9atfxeNjIUF98sknxtatW405c+YYnTt3NrZu3Wps3brVOHbsmGEYZA2xs3TpUiMjI8N46qmnjIqKCmP69OlGp06djI8//jjeRUMSOXbsmKfekmTMmzfP2Lp1q/HJJ58YhmEYDz30kJGXl2e88MILxs6dO41rr73WKCwsNGpqajyvMWXKFOPUU081Xn31VWPLli3G6NGjjcGDBxtNTU3x+lhIMLfddpuRl5dnvP766z7tstraWs86ZM05dMBgu0WLFhmSAv7z9sknnxiXXXaZkZ2dbXTr1s2YNm2azzDghmEYO3bsMEaOHGlkZmYaBQUFxuzZsxkWHD5uuummgFl77bXXPOuQNcTK7373O6NPnz5Gx44djXPPPdczpDNg1muvvRawDrvpppsMw2gdHvy+++4zCgoKjMzMTOPCCy80du7c6fMaX375pTFt2jSjW7duRnZ2tvGtb33L2LNnTxw+DRJVsHbZokWLPOuQNee4DOOrO80BAAAAADHFPWAAAAAA4BA6YAAAAADgEDpgAAAAAOAQOmAAAAAA4BA6YAAAAADgEDpgAAAAAOAQOmAAAAAA4BA6YAAAAADgEDpgAAAAAOAQOmAAAAAA4BA6YAAARODo0aNyuVxav369JOlf//qXzjzzTM2cOVOGYcS5dACAREUHDACACGzfvl0ul0tnn3221q1bpwsvvFAzZ87UQw89JJfLFe/iAQASVId4FwAAgGS0fft29evXT8uXL9ePfvQjPf/887roooviXSwAQILjDBgAABHYvn27qqqqdNNNN6lHjx765je/Ge8iAQCSAB0wAAAisH37dg0dOlRr1qzRzp079Ze//CXeRQIAJAGXwZ3CAABY0tzcrM6dO2vZsmW6/PLLdfXVV6uiokI7duxQWhrHNgEAwbGXAADAovfff191dXUaMmSIJOlnP/uZKioq9Mc//jG+BQMAJDw6YAAAWLR9+3Z17dpVp512miSpuLhYV155pebMmaPm5uY4lw4AkMi4BBEAAAAAHMIZMAAAAABwCB0wAAAAAHAIHTAAAAAAcAgdMAAAAABwCB0wAAAAAHAIHTAAAAAAcAgdMAAAAABwCB0wAAAAAHAIHTAAAAAAcAgdMAAAAABwCB0wAAAAAHAIHTAAAAAAcMj/Bw4sWoesoxQcAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "N = 8000  # total length of signal\n",
    "P = 100  # period\n",
    "K = 250  # upper/lower limit for lag in ACF\n",
    "\n",
    "# generate periodic random signal\n",
    "np.random.seed(1)\n",
    "x0 = np.random.normal(size=P)\n",
    "x = np.tile(x0, N // P)\n",
    "\n",
    "# compute and truncate ACF\n",
    "acf = 1 / len(x) * np.correlate(x, x, mode=\"full\")\n",
    "acf = acf[(len(x) - 1) - (K - 1) : (len(x) - 1) + K]\n",
    "kappa = np.arange(-(K - 1), K)\n",
    "\n",
    "# plot signal and its ACF\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.stem(x[: 2 * K], basefmt=\"C0:\")\n",
    "plt.xlim(0, 2 * K)\n",
    "plt.xlabel(r\"$k$\")\n",
    "plt.ylabel(r\"$x[k]$\")\n",
    "plt.grid()\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.stem(kappa, acf, basefmt=\"C0:\")\n",
    "plt.xlabel(r\"$\\kappa$\")\n",
    "plt.ylabel(r\"$\\hat{\\varphi}_{xx}[\\kappa]$\")\n",
    "plt.axis([-K, K, 1.1 * min(acf), 1.1 * max(acf)])\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**\n",
    "\n",
    "* What period $P$ does the periodic random signal have?\n",
    "\n",
    "Solution: The period of the random signal can be estimated from the ACF, as both, the signal and its ACF have the same periodicity. Inspection is very convenient with the ACF, where the distance between two adjacent peaks reveals the period in samples, here $P=100$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example - Estimating the Pitch of a Speech Signal\n",
    "\n",
    "Speech signals are random signals with specific statistical properties that can be related to their production process in the human [vocal tract](https://en.wikipedia.org/wiki/Vocal_tract). To generate vocals, the sound produced by the periodically vibrating vocal folds is filtered by the resonance volumes and articulators above the voice box. \n",
    "\n",
    "<audio src=\"../data/vocal_o.wav\" controls>Your browser does not support the audio element.</audio>[../data/vocal_o.wav](../data/vocal_o.wav)\n",
    "\n",
    "A vocal captured by a microphone generates consequently a signal which is in good approximation periodic. The [fundamental frequency](https://en.wikipedia.org/wiki/Fundamental_frequency) of a periodic signal is given by the inverse of its period time $T_0 = \\frac{P}{f_s}$, where $f_s$ denotes the sampling frequency. [Pitch detection](https://en.wikipedia.org/wiki/Pitch_detection_algorithm) algorithms aim at estimating the individual fundamental frequency of speech. One common technique is to estimate the average period from the period of the ACF. The following example estimates and plots the ACF of a recorded vocal 'o'. The ACF is plotted as a continuous line for ease of illustration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.io import wavfile\n",
    "\n",
    "K = 200  # upper/lower limit for lag in ACF\n",
    "\n",
    "# read audio file\n",
    "fs, x = wavfile.read(\"../data/vocal_o_8k.wav\")\n",
    "# wav stored as 16Bit integer, convert it to float\n",
    "x = np.asarray(x, dtype=float) / 2**15\n",
    "\n",
    "# compute and truncate ACF\n",
    "acf = 1 / len(x) * np.correlate(x, x, mode=\"full\")\n",
    "acf = acf[(len(x) - 1) - (K - 1) : (len(x) - 1) + K]\n",
    "kappa = np.arange(-(K - 1), K)\n",
    "\n",
    "# plot ACF\n",
    "plt.figure(figsize=(10, 8))\n",
    "plt.plot(kappa, acf)\n",
    "plt.xlabel(r\"$\\kappa$\")\n",
    "plt.ylabel(r\"$\\hat{\\varphi}_{xx}[\\kappa]$\")\n",
    "plt.axis([-K, K, 1.1 * min(acf), 1.1 * max(acf)])\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**\n",
    "\n",
    "* Is the speech signal uncorrelated or correlated?\n",
    "* Estimate the average fundamental frequency $f_0$ of the vocal from its ACF (sampling frequency $f_\\mathrm{s} = 8$  kHz, sampling period $T_s = \\frac{1}{f_s} = 0.125$ ms)\n",
    "\n",
    "Solution: The speech signal is somehow correlated since $\\varphi_{xx}[\\kappa] \\neq 0$ for $\\kappa \\neq 0$. The fundamental frequency may be estimated from the period $P \\approx 80$ of the ACF. This corresponds to a period time of $T_0 = P \\cdot T_s = \\frac{P}{f_s} = \\frac{80}{8000\\,\\mathrm{Hz}} = 0.01\\,\\mathrm{s}$. This yields the fundamental frequency $f_0 = \\frac{1}{T_0} = 100$ Hz."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Auto-Covariance Function\n",
    "\n",
    "The [auto-covariance function](https://en.wikipedia.org/wiki/Covariance) is defined as the ACF of a zero-mean random signal. For a random signal $x[k]$ with linear mean $\\mu_x \\neq 0$ it is given as\n",
    "\n",
    "\\begin{equation}\n",
    "\\psi_{xx}[\\kappa] = \\varphi_{xx}[\\kappa] - \\mu_x^2.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cross-Correlation Function\n",
    "\n",
    "The cross-correlation function (CCF) is a measure of similarity that two random signals $x[k]$ and $y[k]$ exhibit in a statistical sense."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Definition\n",
    "\n",
    "For two continuous-amplitude, real-valued random signals $x[k]$ and $y[k]$ the CCF is defined by the [second-order ensemble average](ensemble_averages.ipynb#Second-Order-Ensemble-Averages) at two different time-instants $k_x$ and $k_y$\n",
    "\n",
    "\\begin{equation}\n",
    "\\varphi_{xy}[k_x, k_y] = E\\{ x[k_x] \\cdot y[k_y] \\}.\n",
    "\\end{equation}\n",
    "\n",
    "Under the assumption of [wide-sense stationarity](stationary_ergodic.ipynb#Wide-Sense-Stationary-Random-Processes) (WSS) the CCF does only depend on the difference $\\kappa = k_x - k_y$ between the considered sample indices\n",
    "\n",
    "\\begin{equation}\n",
    "\\varphi_{xy}[\\kappa] = E\\{x[k] \\cdot y[k - \\kappa] \\} = E\\{x[k + \\kappa] \\cdot y[k] \\}.\n",
    "\\end{equation}\n",
    "\n",
    "The cross-correlation function (CCF) is a measure of similarity that two random signals $x[k]$ and $y[k - \\kappa]$ have with respect to the time shift / lag $\\kappa \\in \\mathbb{Z}$. If $x[k]$ and $y[k]$ originate from wide-sense ergodic processes, the CCF can be computed by averaging along one sample function each as\n",
    "\n",
    "\\begin{equation}\n",
    "\\varphi_{xy}[\\kappa] = \\lim_{K \\to \\infty} \\frac{1}{2K + 1} \\sum_{k=-K}^{K} x[k] \\cdot y[k-\\kappa].\n",
    "\\end{equation}\n",
    "\n",
    "For finite length random signals $x_N[k] = \\text{rect}_N[k] \\cdot x[k]$ (assigning length $N$ to $x$) and $y_M[k] = \\text{rect}_M[k] \\cdot y[k]$ (assigning length $M$ to $y$) one yields\n",
    "\n",
    "\\begin{equation}\n",
    "\\varphi_{xy}[\\kappa] := \\frac{1}{N} \\sum_{k=0}^{N-1} x_N[k] \\cdot y_M[k-\\kappa] = \\frac{1}{N} \\; x_N[\\kappa] * y_M[- \\kappa],\n",
    "\\end{equation}\n",
    "\n",
    "where the CCF $\\varphi_{xy}[\\kappa] = 0$ for $\\kappa < -(M-1)$ and $\\kappa > N-1$. The CCF can be computed by (fast) convolution of one random signal with a time reversed version of the other random signal. The connections between the linear convolution and the cross-correlation of two signals allows an interesting interpretation of linear time-invariant (LTI) systems. An LTI system correlates the input signal with the time reversed impulse response in order to generate the output signal.\n",
    "\n",
    "Note that in numerical implementations (e.g. MATLAB, Python with `mode='full'`), the computed ACF is stored in a vector of length $N + M - 1$. The positive indices $0, 1, \\dots, N + M - 2$ of this vector cannot be directly interpreted as $\\kappa$. \n",
    "For interpretation with respect to the actual time lag $\\kappa$, $M-1$ must be subtracted  from these indices. Above results hold also for the CCF $\\varphi_{yx}[\\kappa]$ when exchanging $x[k]$ with $y[k]$ and $N$ with $M$.\n",
    "\n",
    "Further note that $\\frac{1}{N}$-averaging is a convention chosen here to be consistent with above introduced temporal averaging concept. The common choice for $N=M$ yields the biased estimator for the CCF, but special care on the interpretation is required if $N\\neq M$.\n",
    "\n",
    "If $x$ and $y$ are just swapped (i.e. $x$ is of length $M$, $y$ of length $N$ then), the result differs in terms of the time alignment and for the amplitude values of the CCF. The latter is due to $\\frac{1}{N}$-averaging. See the simple example below, where in the first case, $N=3$ and $M=4$ and thus averaging with $\\frac{1}{3}$, whereas in the second case, $N=4$ and $M=3$ deploys averaging by $\\frac{1}{4}$. It is worth to check the two different time alignments then."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1100x300 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(11, 3))\n",
    "\n",
    "plt.subplot(1, 2, 1)  # case 1: x shorter than y\n",
    "x = (1, -1, 1)\n",
    "y = (1, -1, -1, 1)\n",
    "N = len(x)\n",
    "M = len(y)\n",
    "xc1 = 1 / N * np.correlate(x, y, mode=\"full\")\n",
    "kappa1 = np.arange(0, N + M - 1) - (M - 1)\n",
    "plt.stem(kappa1, xc1, basefmt=\"C0:\")\n",
    "plt.xlabel(r\"$\\kappa$\")\n",
    "plt.ylabel(r\"$\\hat{\\varphi}_{xy}[\\kappa]$\")\n",
    "plt.title(r\"$N_x$=\" + str(N) + \", $M_y$=\" + str(M))\n",
    "plt.ylim(-1, 1)\n",
    "plt.grid(True)\n",
    "\n",
    "plt.subplot(1, 2, 2)  # case 2: x longer than y\n",
    "y, x = x, y  # elegant variable swap\n",
    "N, M = M, N\n",
    "xc2 = 1 / N * np.correlate(x, y, mode=\"full\")\n",
    "kappa2 = np.arange(0, N + M - 1) - (M - 1)\n",
    "plt.stem(kappa2, xc2, basefmt=\"C0:\")\n",
    "plt.xlabel(r\"$\\kappa$\")\n",
    "plt.ylabel(r\"$\\hat{\\varphi}_{xy}[\\kappa]$\")\n",
    "plt.title(r\"$N_x$=\" + str(N) + \", $M_y$=\" + str(M))\n",
    "plt.ylim(-1, 1)\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Properties\n",
    "\n",
    "1. When exchanging the two random signals, the CCF exhibits the following symmetry \n",
    "\n",
    "    $$ \\varphi_{xy}[\\kappa] = \\varphi_{yx}[-\\kappa] $$\n",
    "    \n",
    "2. For typical random processes, the CCF approaches the limiting value\n",
    "\n",
    "    $$ \\lim_{|\\kappa| \\to \\infty} \\varphi_{xy}[\\kappa] = \\mu_x \\cdot \\mu_y$$\n",
    "\n",
    "Two random signals are said to be [**uncorrelated**](https://en.wikipedia.org/wiki/Uncorrelated_random_variables) if\n",
    "    \n",
    "\\begin{equation}\n",
    "\\varphi_{xy}[\\kappa] = \\mu_x \\cdot \\mu_y\n",
    "\\end{equation}\n",
    "\n",
    "and as correlated if this condition is not met. The samples of two signals which are uncorrelated to each other show no dependencies between each other in a statistical sense. $\\varphi_{xy}[\\kappa] = 0$ for uncorrelated signals if one of the two random processes exhibits zero-mean."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example - Time-of-Arrival Estimation\n",
    "\n",
    "The CCF can be used to estimate the [time-of-arrival (TOA)](https://en.wikipedia.org/wiki/Time_of_arrival) of a signal transmitted from a sender to a receiver. The TOA is used for instance for [radiolocation](https://en.wikipedia.org/wiki/Radiolocation) or sound source localization. For ease of illustration it is assumed that a random signal $x[k]$ is only delayed by the transmission channel. The received signal $y[k]$ is then just a delayed version of transmitted signal\n",
    "\n",
    "\\begin{equation}\n",
    "y[k] = x[k - k_0] = x[k] * \\delta[k - k_0].\n",
    "\\end{equation}\n",
    "\n",
    "The aim is to estimate the delay $k_0$ by observation of the received signal under knowledge of the transmitted signal. Under the assumption of finite length signals, the CCF between the transmitted and the received signal is given as\n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "\\varphi_{xy}[\\kappa] &= \\frac{1}{N} x_N[\\kappa] * y_M[-\\kappa] \\\\\n",
    "&= \\frac{1}{N} \\left( x_N[\\kappa] * x_N[-\\kappa] \\right) * \\delta[-k+k_0] \\\\\n",
    "&= \\frac{1}{N} \\varphi_{xx}[\\kappa] * \\delta[k - k_0],\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "\n",
    "where the associativity of the convolution and the even symmetry of the Dirac pulse has been used. The delay between the two signals results in a shift of the ACF of the transmitted signal. The delay can be estimated by finding the maximum value of the CCF $\\varphi_{xy}[\\kappa]$, if the ACF $\\varphi_{xx}[\\kappa]$ of the transmitted signal $x[k]$ exhibits a pronounced maximum at $\\kappa = 0$\n",
    "\n",
    "\\begin{equation}\n",
    "\\hat{k}_0 = \\underset{\\kappa}{\\mathrm{argmax}} \\{ \\varphi_{xy}[\\kappa] \\}.\n",
    "\\end{equation}\n",
    "\n",
    "One can differentiate between to types of transmitted signals: (i) ones which have been designed explicitly for TOA estimation and (ii) application specific signals. The latter are for instance wireless or speech signals which are used in the applications where specific measurement signals may not be appropriate. For the former, there exist various choices for finite length random sequences with good auto-correlation properties.\n",
    "\n",
    "The Gold code is a pseudo random noise (PRN) sequence used in the [Global Positioning System (GPS)](https://en.wikipedia.org/wiki/Global_Positioning_System) to estimate the TOA between satellites and a GPS receiver. It constitutes a series of binary sequences with good auto- and cross-correlation properties. The latter is required to lower the interference between the sequences of different GPS satellites. The properties of these specific random signals are investigated and the application of these sequences to TOA estimation is illustrated. First the pre-computed sequences are loaded and a function for computing and plotting the CCF (and ACF) is defined for convenience"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# load set of PRN sequences (Gold codes)\n",
    "prn = np.load(\"../data/gold_sequences.npz\")[\"prn\"]\n",
    "\n",
    "\n",
    "def compute_plot_CCF(x, y, ylabel, K=30):\n",
    "    \"\"\"Computes, truncates and plots CCF.\"\"\"\n",
    "    ccf = 1 / len(x) * np.correlate(x, y, mode=\"full\")\n",
    "    ccf = ccf[(len(y) - 1) - K : len(y) + K]\n",
    "    kappa = np.arange(-K, K + 1)\n",
    "\n",
    "    # plot CCF\n",
    "    plt.stem(kappa, ccf, basefmt=\"C0:\")\n",
    "    plt.xlabel(r\"$\\kappa$\")\n",
    "    plt.ylabel(ylabel)\n",
    "    plt.axis([-K, K, 1.1 * min(ccf), 1.1 * max(ccf)])\n",
    "    plt.grid()\n",
    "\n",
    "    return ccf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The ACF for one particular PRN sequence (one sample function) and the CCF between two different PRN sequences is computed and plotted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 4))\n",
    "\n",
    "plt.subplot(121)\n",
    "xi = yi = 10  # CCF\n",
    "compute_plot_CCF(prn[xi, :], prn[yi, :], r\"$\\hat{\\varphi}_{x_n x_n}[\\kappa]$\")\n",
    "plt.title(\"ACF of one pseudo random noise sequence\")\n",
    "\n",
    "plt.subplot(122)\n",
    "xi, yi = 10, 16  # ACF\n",
    "compute_plot_CCF(prn[xi, :], prn[yi, :], r\"$\\hat{\\varphi}_{x_n y_m}[\\kappa]$\")\n",
    "plt.title(\"CCF between two pseudo random noise sequences\")\n",
    "plt.ylim([-1, 1])\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The ACF features a pronounced peak for $\\kappa = 0$ and thus the two PRN sequences are reasonably uncorrelated. Now, one particular sequence is delayed in order to model the received signal. The CCF is plotted and the TOA is estimated by finding the maximum value of the CCF between the transmitted and received sequence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated TOA delay is 15 samples\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k0 = 15  # true TOA delay in samples\n",
    "K = 30  # upper/lower limit for lag in ACF\n",
    "\n",
    "x = prn[16, :]  # pick one PRN sequence, sender, source signal\n",
    "y = x[k0:]  # delay transmitted signal by k0 samples, receiver, sink signal\n",
    "\n",
    "# compute and plot CCF\n",
    "plt.figure(figsize=(10, 4))\n",
    "ccf = compute_plot_CCF(x, y, r\"$\\hat{\\varphi}_{xx}[\\kappa]$\", K=K)\n",
    "plt.title(\"CCF between transmitted and received signal\")\n",
    "\n",
    "# estimate the TOA\n",
    "print(\"Estimated TOA delay is {:2.0f} samples\".format(np.argmax(ccf) - K))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**\n",
    "\n",
    "* Add a random signal with different levels to the received signal. How does this influence the TOA estimation?\n",
    "\n",
    "Solution: Additive noise can be added for instance by extending above example with `y = y + 0.1 * np.random.normal(len(y))`. Additive noise corrupts the CCF. For high levels, the maximum value of the CCF might not correspond to the delay $k_0$ anymore."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example - Cross-Correlation Function of Two Random Signals\n",
    "\n",
    "The following example estimates and plots the CCF of two random signals $x[k]$ and $y[k]$ of finite lengths $N$ and $M = 2 N$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean of signal x[k]: 2.02\n",
      "Mean of signal y[k]: 3.06\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "L = 2**8  # length\n",
    "\n",
    "# generate two uncorrelated random signals\n",
    "np.random.seed(1)\n",
    "x = 2 + np.random.normal(size=L // 4)\n",
    "y = 3 + np.random.normal(size=L * 2)\n",
    "\n",
    "# compute CCF\n",
    "ccf = 1 / len(x) * np.correlate(x, y, mode=\"full\")  # biased estimator\n",
    "kappa = np.arange(0, len(x) + len(y) - 1) - (len(y) - 1)\n",
    "# ccf = L/(L-np.abs(kappa)) * ccf  # unbiased estimator, only if len(x)==len(y)\n",
    "\n",
    "# print mean values of signals\n",
    "print(\"Mean of signal x[k]: %3.2f\" % np.mean(x))\n",
    "print(\"Mean of signal y[k]: %3.2f\" % np.mean(y))\n",
    "\n",
    "# plot CCF\n",
    "plt.figure(figsize=(10, 8))\n",
    "plt.stem(kappa, ccf, basefmt=\"C0:\", linefmt=\"C0:\")\n",
    "plt.title(\n",
    "    \"Biased estimator of cross-correlation function, N=\"\n",
    "    + str(len(x))\n",
    "    + \", M=\"\n",
    "    + str(len(y))\n",
    ")\n",
    "plt.ylabel(r\"$\\hat{\\varphi}_{xy}[\\kappa]$\")\n",
    "plt.xlabel(r\"$\\kappa$\")\n",
    "plt.axis([kappa[0], kappa[-1], 0, 1.1 * max(ccf)])\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**\n",
    "\n",
    "* Can the signals be assumed to be correlated or uncorrelated when considering the CCF in the range $-M < \\kappa < 0$ only?\n",
    "* Why does the CCF of the two finite length signals have this overall trapezoid like shape? \n",
    "* What would be its theoretic value for signals of infinite length?\n",
    "\n",
    "Solution: The CCF is approximately constant for $-M < \\kappa < 0$. Consequently, the random signals $x[k]$ and $y[k]$ can be assumed to be uncorrelated. The trapezoidal shape of the CCF results from the truncation of the random signals to a finite number of samples. This truncation can be modeled as a multiplication of the infinite length signals by a rectangular signal $\\text{rect}_N[k]$ and $\\text{rect}_M[k]$, respectively. Interpreting the CCF as convolution and having in mind that the convolution of two rectangular signals results in a signal of trapezoidal shape explains the shape of the CCF shown above. Its theoretic value is constant with a value given by the multiplication of the two linear means of the random signals $\\varphi_{xy}[\\kappa] = \\mu_x \\cdot \\mu_y$, here 6."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cross-Covariance Function\n",
    "\n",
    "The [cross-covariance function](https://en.wikipedia.org/wiki/Covariance) is defined as the CCF of two zero-mean random signals. For two random signals $x[k]$ and $y[k]$ with linear means $\\mu_x \\neq 0$ and $\\mu_y \\neq 0$ it is given as\n",
    "\n",
    "\\begin{equation}\n",
    "\\psi_{xy}[\\kappa] = \\varphi_{xy}[\\kappa] - \\mu_x \\cdot \\mu_y\n",
    "\\end{equation}\n",
    "\n",
    "The properties of the CCF yield that the cross-covariance function $\\psi_{xy}[\\kappa]$ of two uncorrelated signals $x[k]$ and $y[k]$ is zero, i.e. $\\psi_{xy}[\\kappa] = 0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**\n",
    "\n",
    "* What would the plot for $\\psi_{xy}[\\kappa]$ look like for the [example above](#Example---Cross-Correlation-Function-of-Two-Random-Signals) under the assumption of finite length signals?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbsphinx": "hidden"
   },
   "source": [
    "**Copyright**\n",
    "\n",
    "This notebook is provided as [Open Educational Resource](https://en.wikipedia.org/wiki/Open_educational_resources). Feel free to use the notebook for your own purposes. The text is licensed under [Creative Commons Attribution 4.0](https://creativecommons.org/licenses/by/4.0/), the code of the IPython examples under the [MIT license](https://opensource.org/licenses/MIT). Please attribute the work as follows: *Sascha Spors, Digital Signal Processing - Lecture notes featuring computational examples*."
   ]
  }
 ],
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